Statistical Analysis with Measurement Error or Misclassification

Abstract

This monograph on measurement error and misclassification covers a broad range of problems and emphasizes unique features in modeling and analyzing problems arising from medical research and epidemiological studies. Many measurement error and misclassification problems have been addressed in various fields over the years as well as with a wide spectrum of data, including event history data (such as survival data and recurrent event data), correlated data (such as longitudinal data and clustered data), multi-state event data, and data arising from case-control studies. Statistical Analysis with Measurement Error or Misclassification: Strategy, Method and Application brings together assorted methods in a single text and provides an update of recent developments for a variety of settings. Measurement error effects and strategies of handling mismeasurement for different models are closely examined in combination with applications to specific problems. Readers with diverse backgrounds and objectives can utilize this text. Familiarity with inference methods--such as likelihood and estimating function theory--or modeling schemes in varying settings--such as survival analysis and longitudinal data analysis--can result in a full appreciation of the material, but it is not essential since each chapter provides basic inference frameworks and background information on an individual topic to ease the access of the material. The text is presented in a coherent and self-contained manner and highlights the essence of commonly used modeling and inference methods. This text can serve as a reference book for researchers interested in statistical methodology for handling data with measurement error or misclassification; as a textbook for graduate students, especially for those majoring in statistics and biostatistics; or as a book for applied statisticians whose interest focuses on analysis of error-contaminated data. Grace Y. Yi is Professor of Statistics and University Research Chair at the University of Waterloo. She is the 2010 winner of the CRM-SSC Prize, an honor awarded in recognition of a statistical scientist's professional accomplishments in research during the first 15 years after having received a doctorate. She is a Fellow of the American Statistical Association and an Elected Member of the International Statistical Institute. Preface; About the Author; Contents; 1 Inference Framework and Method ; 1.1 Framework and Objective; 1.2 Modeling and Estimator; 1.2.1 Parameter and Identifiability; 1.2.2 Parameter Estimator; 1.2.3 Concepts in Asymptotic Sense; 1.3 Estimation Methods; 1.3.1 Likelihood Method; 1.3.2 Estimating Equations; 1.3.3 Generalized Method of Moments; 1.3.4 Profiling Method; 1.4 Model Misspecification; 1.5 Covariates and Regression Models; 1.6 Bibliographic Notes and Discussion; 1.7 Supplementary Problems; 2 Measurement Error and Misclassification: Introduction. 2.1 Measurement Error and Misclassification2.2 An Illustration of Measurement Error Effects; 2.3 The Scope of Analysis with Mismeasured Data; 2.4 Issues in the Presence of Measurement Error; 2.5 General Strategy of Handling Measurement Error ; 2.5.1 Likelihood-Based Correction Methods; 2.5.2 Unbiased Estimating Functions Methods; 2.5.3 Methods of Correcting Naive Estimators; 2.5.4 Discussion; 2.6 Measurement Error and Misclassification Models; 2.7 Measurement Error and Misclassification Examples; 2.7.1 Survival Data Example: Busselton Health Study; 2.7.2 Recurrent Event Example: rhDNase Data. 2.7.3 Longitudinal Data Example: Framingham HeartStudy2.7.4 Multi-State Model Example: HL Data; 2.7.5 Case-Control Study Example: HSV Data; 2.8 Bibliographic Notes and Discussion; 2.9 Supplementary Problems; 3 Survival Data with Measurement Error; 3.1 Framework of Survival Analysis: Models and Methods; 3.1.1 Basic Measures; 3.1.2 Some Parametric Modeling Strategies; 3.1.3 Regression Models; 3.1.4 Special Features of Survival Data; 3.1.5 Likelihood Method; 3.1.6 Model-Dependent Inference Methods; 3.2 Measurement Error Effects and Inference Framework; 3.2.1 Induced Hazard Function. 3.2.2 Discussion and Assumptions3.3 Approximate Methods for Measurement Error Correction; 3.3.1 Regression Calibration Method; 3.3.2 Simulation Extrapolation Method; 3.4 Methods Based on the Induced Hazard Function; 3.4.1 Induced Likelihood Method; 3.4.2 Induced Partial Likelihood Method; 3.5 Likelihood-Based Methods; 3.5.1 Insertion Correction: Piecewise-Constant Method; 3.5.2 Expectation Correction: Two-Stage Method; 3.6 Methods Based on Estimating Functions; 3.6.1 Proportional Hazards Model; 3.6.2 Simulation Study; 3.6.3 Additive Hazards Model; 3.6.4 An Example: Analysis of ACTG175 Data. 3.7 Misclassification of Discrete Covariates3.7.1 Methods with Known Misclassification Probabilities; 3.7.2 Method with a Validation Sample; 3.7.3 Method with Replicates; 3.8 Multivariate Survival Data with Covariate MeasurementError; 3.8.1 Marginal Approach; 3.8.2 Dependence Parameter Estimation of Copula Models; 3.8.3 EM Algorithm with Frailty Measurement ErrorModel; 3.9 Bibliographic Notes and Discussion; 3.10 Supplementary Problems; 4 Recurrent Event Data with Measurement Error ; 4.1 Analysis Framework for Recurrent Events; 4.1.1 Notation and Framework.